Homework 12. December 7, 2011

Transcription

1 Homework 12 December 7, Chapter Humans are the crown of creation and an inevitable result of billions of years of evolution I would disagree with this claim. First of all, I would argue that no species (or type of species) can really be an inevitable result of evolution. The trajectory of evolution is governed in part by the environment and by chance. Further, there are many highly adapted species that have not evolved intelligence, and in class we talked about how it is plausible that our intelligence evolved as an adaption to life in trees. Although it is not absurd to think that there might be environments on other planets that also favor the evolution of intelligent life, this hardly seems to suggest that it is something universal. 16, If, for some reason, we humans were to suddenly wipe out our species, another species - possibly the raccoons - would soon evolve greater intelligence than we possessed. I don t think there is any reason to believe this, given what was discussed in the above question. In particular, there is no rule that says evolution has to culminate with the rise of a civilization, or that there always has to be an intelligent species or a species on its way to intelligence. 17. Sea creatures, no matter how clever they are, could never master the technology required to communicate with other worlds. I think this is a pretty reasonable idea. I might hesitate to say that it is definitively impossible for sea creatures to master technology, but we are not aware of any sea creatures that have the ability to manipulate tools in the manner that would be necessary. Octopuses or squids offer probably the best examples, but tentacles don t really even compare to the usefulness of hangs in using tools and manipulating one s environment. There are also difficulties associated with the water itself, it would certainly be more difficult to build electronics for example, however I don t think the extent of this difficulty is entirely clear. 19. Because SETI researchers are listening to star systems that are hundreds of light-years distant, there s good chance that by the time 1

2 we hear a signal, the civilization that sent it will have disappeared This one is a little bit tricky. In part, the answer depends on what you think the average lifetime of an advanced civilization would be. The question specifies stars that are hundreds of light years away. I think most people would expect civilizations capable of broadcasting to last at least a few hundred years. For instance, I think most people would expect humans to still be around a few hundred years from now. However, that being said, it is worth considering that a civilization could disappear in the time it takes for a message to reach us. 1.1 Multiple Choice 25. The end of a calculation with the Drake equation is intended to be an estimate of (b) the number of worlds in the galaxy on which intelligence has arisen 26. Which of the following statements is true about the terms in the Drake equation? (b) Some of the terms depend on sociology and cannot be determined by astronomers alone. 29. The bandwidth of a radio signal is a measure of (b) the range of frequencies that carry information. 30. Why are we more likely to be able to detect a deliberately broadcast beacon signal than, say, the television broadcasts of a distant civilization? (b) because our current technology is probably sensitive enough to detect beacons but not much weaker television transmissions. 31. What is the distinguishing characteristic that those doing radio SETI experiments look for? ( c) a signal that extends over only a very narrow band of frequencies. 32. Two-way conversation with other societies is probably unlikely, even if we make contact. This is mainly because ( c) The time it takes for signals to cross the distance to them could be centuries or more. 1.2 Quantitative 43. The number of stars to search? The number of star systems that a SETI search would have to investigate before achieving success depends on how common signaling societies are in the galaxy. This is the number estimated by the Drake equation. Suppose this number is N = 1 million. How many star systems must be checked out by SETI in order to find one signal? What if N = 1000? Assume that there are roughly 100 billion stars in our galaxy. Naively, we can say that if only one out of every X planets has a communicating civilization we should expect 2

3 to have to search X planets to find one. Here, X is just N /N = /N. Then, in the first case we have and in the second case X = 1011 = 100, 000 stars 106 X = 1011 = 100 million stars 1000 If we want to be a little bit more sophisticated we can calculate the probability of finding an intelligent civilization after searching X stars, assuming that the civilizations are uniformly distributed throughout the galaxy. The method of doing this kind of calculation will be familiar to anyone who has ever encountered the birthday paradox. In our case, if we search a random star the probability of it hosting a communicating civilization is P = N Now, we will want to consider 1 P the probability of not finding a civilization after scanning a given star. Then, the probability of not finding a civilization after searching X stars is just given by (1 P ) X So, the probability of finding a civilization is given by P X = 1 (1 P ) X Then, in the two cases above we have P = 10 5 and P = Now, we can plug in the values of X that we found above to see what the probability would actually be after searching X planets in each case. For the first case and in the second case 1 ( ) 100,000 = 63.2% 1 ( ) 100,000,000 = 63.2% One should keep in mind that the result won t be 63.2 percent for every possible value of N. The function that we are considering here is 1 (1 1 x )x This function isn t constant but it does have an asymptote around 63.2 percent, as we can see from the plot 3

4 We can also plot the probability of finding a civilization after X searches for some fixed value of N (we will take 1 million as in the first case). We get, Chapter A brilliant teenager working in her garage discovers a way to build a rocket that burns coal as its fuel and can travel at half the speed of light. This is very implausible. We talked about the limitations of chemical fuel in class. No matter how clever you are there is just not enough energy to build that kind of rocket. 22. Using beamed energy propulsion from a laser powered by energy produced at a windmill farm in the California desert, NASA engineers are able to send a solar sailing ship on a journey to Alpha Centauri that will take only 50 years. The idea of using a laser to power an interstellar space ship was explored in the text. While the concept is fairly sound and the numbers given in the above statement seem fine, there is no way a windmill farm would be able to produce the required energy. 4

5 23. Human colonization of the moons of Saturn occurs using spaceships powered by dropping nuclear booms out the back of the ships. The text explores this idea as well and concludes that it is actually a more or less sound idea for travel within the solar system. So, this one is plausible. 24. In the year 2750, we receive a signal from a civilization around a nearby star telling us that the Voyager 2 spacecraft recently crashlanded on its planet. The voyager 2 doesn t travel fast enough to reach a nearby star within a few hundred years, also the chances of it crash landing on a planet are pretty small. 25. The General Rocket Corporation (a future incarnation of General Motors) unveils a new personal interstellar spacecraft that works as an interstellar ramjet with a scoop about 10 meters. The scoop is not nearly big enough to be effective. We talked about this in class, the scoop would have to be hundreds of kilometers across. 26. Members of the first crew of the matter-antimatter spacecraft STar Apollo, which left Earth in the year 2165, return to Earth in the year 2450 looking only a few years older than when they left. This is plausible because of the time dilation effect of special relativity. Depending on how close to the speed of light they were traveling, they could experience the whole trip in only a few years even if it takes a hundred years from our perspective. 27. Im the year 2011, we finally uncover definitive evidence of alien visits to Earth when a flying saucer crashes in the Rocky Mountains and its oxygen-kerosene fuel ignites a forest fire. It is highly implausible that the aliens would still be using chemical fuel. I suppose the flying saucer could be a small ship sent to land on Earth from a larger mothership with a different fuel supply. However, they would probably have much better methods of powering even their small spacecraft. 2.1 Multiple Choice 31. The New Horizons spacecraft is currently on its way to Pluto and will eventually continue out of our solar system. About how long will it take to travel the distance ego the nearest stars? ( c) 100,000 years 35. Suppose that a spaceship was launched in the year 2120 on a round-trip journey of 100 light-years, traveling at 99.99%the speed of light. If one of the crew members was 30 years old when she left, about how old would you expect her to be on her return? (a) 31 5

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